Systems that are described by the nonlinear differential equations are omnipresent ranging from biological systems to physical systems and economics[1]}, [2]}, [3]}. The nonlinearities present in these systems facilitate the emergence of rich dynamical states such as self-sustained oscillations, turbulence, and chaos, which are impossible to obtain in the systems described by the linear differential equations. In particular, one of the important characteristics of nonlinear differential equations is the amplitude-dependent frequency of nonlinear oscillations, known as nonisochronicity, the term first used in ref.[4]}. Nonisochronicity is central to inhomogeneities that can be seen in a variety of living situations [5]}, [6]} and due to this nonisochronous nature of the nonlinear equations, different responses have been observed for different input conditions in practical or experimental settings. In particular, when considering the complex biological or other networks, the strong nonisochronicity often results in rich synchronization patterns and the level of isochronicity of oscillators is an important property of the phase interaction function, where the strong dependence of the oscillatory period or frequency on the amplitude results in high-level shear in the phase dynamics and coupling can dramatically change the oscillatory period[7]}. Also, it has been reported that the higher nonisochronicity level can induce long, irregular transient phase dynamics in the networks, where such long transient dynamics have relevance in the functioning of biological systems[8]}. The detection of isochrons in a system is also prescribed recently[9]}, [10]}. Moreover, nonisochronicity plays a significant role in the development of anomalous phase synchronization in populations of nonidentical oscillators[11]}, which has also been experimentally confirmed[12]}, [13]}. Further, in the networks of nonlocally coupled Stuart-Landau oscillators, the nonisochronicity leads to the emergence of various collective states such as amplitude chimera, amplitude cluster, frequency chimera, frequency cluster states, imperfect and mixed imperfect synchronized states, local and global chimera states, etc., which have been recently reported in the case of symmetry preserving and symmetry breaking couplings [14]}, [15]}, [16]}, [17]}, [18]}. Similarly, the emergence of nonisochronicity induced chimera, and chimera-like states in nonlocally and globally coupled complex Ginzburg-Landau model[19]}, [20]}, [21]}, van der Pol
system[22]} are also demonstrated. Furthermore, in ref.[23]}, the authors reported that the nonisochronicity could also be used to control the transition to synchronization in an ensemble of nonidentical oscillators.
